Propagation of chaos for topological interactions

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Title: Propagation of chaos for topological interactions
Authors: Degond, P
Pulvirenti, M
Item Type: Journal Article
Abstract: We consider aN-particle model describing an alignment mechanism due to a topolog-ical interaction among the agents. We show that the kinetic equation, expected to holdin the mean-field limitN→∞, as following from the previous analysis in Ref. [3] can berigorously derived. This means that the statistical independence (propagation of chaos)is indeed recovered in the limit, provided it is assumed at time zero.
Issue Date: 23-Jul-2019
Date of Acceptance: 6-Feb-2019
URI: http://hdl.handle.net/10044/1/67443
DOI: https://doi.org/10.1214/19-AAP1469
ISSN: 1050-5164
Publisher: Institute of Mathematical Statistics
Start Page: 2594
End Page: 2612
Journal / Book Title: Annals of Applied Probability
Volume: 29
Issue: 4
Copyright Statement: © Institute of Mathematical Statistics, 2019.
Sponsor/Funder: The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: WM130048
EP/M006883/1
EP/P013651/1
Keywords: Science & Technology
Physical Sciences
Statistics & Probability
Mathematics
Rank-based interactions
Boltzmann equation
BOLTZMANN-GRAD LIMIT
MEAN-FIELD LIMIT
GLOBAL VALIDITY
RARE-GAS
EQUATIONS
SYSTEMS
CONVERGENCE
PARTICLES
FLOCKING
FORCES
math-ph
math-ph
math.MP
Statistics & Probability
0102 Applied Mathematics
0104 Statistics
Publication Status: Published
Online Publication Date: 2019-07-23
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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